The integral of dx / (x^2 - 1)^2 can be approached using partial fraction decomposition and hyperbolic substitution. The substitution x = cosh(t) is recommended for simplifying the expression, as it transforms the integral into a more manageable form. Attempts to use x = sqrt(t) were unsuccessful, indicating that traditional substitutions may not yield results. The discussion emphasizes the importance of recognizing patterns in integrals involving quadratic expressions.
PREREQUISITESStudents and educators in calculus, mathematicians seeking to enhance their integration techniques, and anyone tackling complex integrals involving rational functions.
aija said:Homework Statement
integrate dx / (x^2 - 1)^2
Homework Equations
The Attempt at a Solution
There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get:
∫( dt / (t-1)^2 * 2sqr(t) )
and it's still impossible to integrate.